A random sample of 20 employees was collected from Brac University, to estimate the average daily time they spent on social media. Suppose that the population times have a normal distribution with a mean of 95 minutes and a standard deviation of 23 minutes. a. Find the probability that the sample mean more than 85 minutes.(answer in three decimal places)  b. What is the probability that the sample mean is outside the range of 90 to 100 minutes? (answer in three decimal places)

Suppose the amount of change IWU students carry is exponentially distributed with a mean of $0.88. Suppose that we randomly pick 25 IWU students and learn how much change they have. What type of distribution does the population, which is the change carried by IWU students, follow? What are the mean and standard deviation of the population? (6 points)           What type of distribution does the sample mean follow? What are the mean and standard deviation of the sample mean? (6 points)           Find the probability that the average change of 25 IWU students was between $0.80 and $1.00. Graph the situation, shade in the area to be determined, and find the probability. (6 points)

A common test was given to a no. of students taken at random from a             particular class of the department to assess the significance of possible             variance of performance. Make an analysis of variance  with the given              data:                       A:  5   6   8   9 7                        B:  8 10 11 12 4                        C:  7   3   5   4 1

The standard deviation of the scores on a skill evaluation test is 363 points with a mean of 1239 points. If 335 tests are sampled, what is the probability that the mean of the sample would differ from the population mean by less than 23 points? Round your answer to four decimal places.

The score obtained on an emotional intelligence test is normally distributed,with an average score (μ) of 112 and a standard deviation (σ) of 8.5. What is the probability that a randomly selected person will:Q.6.3.1 Obtain a score between 111 and 116? Interpret your answer. Q.6.3.2 Obtain a score between 107 and 110? Interpret your answer.

A lathe is set to cut bars of steel into lengths of 6 centimeters. The lathe is considered to be in perfect adjustment if the average length of the bars it cuts is 6 centimeters. A sample of 121 bars is selected randomly and measured. It is determined that the average length of the bars in the sample is 6.08 centimeters with a standard deviation of 0.44 centimeters. Compute the p-value for testing whether the population mean is larger than 6 centimeters. NOTE: WRITE YOUR ANSWER WITH 4 DECIMAL DIGITS. DO NOT ROUND UP OR DOWN.

Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined that the population of potential clientele have head breadths that are normally distributed with a mean of 6.6-in and a standard deviation of 0.9-in.In what range would you expect to find the middle 50% of most head breadths? Between _____________ and __________________.If you were to draw samples of size 37 from this population, in what range would you expect to find the middle 50% of most averages for the breadths of male heads in the sample? Between _______________ and ________________.Enter your answers as numbers. Your answers should be accurate to 2 decimal place

A quality control expert at LIFE batteries wants to test their new batteries. The design engineer claims they have a variance of 2601 with a mean life of 1191 minutes. If the claim is true, in a sample of 167 batteries, what is the probability that the mean battery life would be less than 1184.1 minutes? Round your answer to four decimal places.

Americans spend an average of 23.6 hours per week online, with a standard deviation of 7. The distribution of internet watching is not necessarily normally distributed. Suppose you took a random sample of 50 people. What is the probability that the sample average will be less than 23 hrs? Round your answer to three decimal places, eg 0.628.